On the exponent conjecture of Schur

It is a longstanding conjecture that for a finite group \(G\), the exponent of the second homology group \(H_2(G, \mathbb{Z})\) divides the exponent of \(G\). In this paper, we prove this conjecture for \(p\)-groups of class at most \(p\), finite nilpotent groups of odd exponent and of nilpotency cl...

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Bibliographic Details
Published in:arXiv.org 2020-05
Main Authors: Antony, Ammu E, Komma Patali, Thomas, Viji Z
Format: Article
Language:English
Subjects:
Commutators
Homology
Online Access:Get full text
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Summary:It is a longstanding conjecture that for a finite group \(G\), the exponent of the second homology group \(H_2(G, \mathbb{Z})\) divides the exponent of \(G\). In this paper, we prove this conjecture for \(p\)-groups of class at most \(p\), finite nilpotent groups of odd exponent and of nilpotency class 5, \(p\)-central metabelian \(p\)-groups, and groups considered by L. E . Wilson in \cite{LEW}. Moreover, we improve several bounds given by various authors. We achieve most of our results using an induction argument.
ISSN:2331-8422